The Sylow Theorems · Hard problem

A group has order $255=3\cdot5\cdot17$. Sylow III leaves $n_3\in\{1,85\}$ and $n_5\in\{1,51\}$. If BOTH took their larger value ($n_3=85$ and $n_5=51$), how many elements of order $3$ or order $5$ would $G$ need, at minimum?